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Manager  Joined: 24 May 2013
Posts: 76
If k is an integer greater than 6, all of the following must be divisi  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 70% (01:38) correct 30% (01:55) wrong based on 271 sessions

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If k is an integer greater than 6, all of the following must be divisible by 3 EXCEPT

A. k(k + 3)(k - 1)
B. 3k^3
C. (k+1)(k+5)(k+6)
D. (k+2)(k-2)(k+3)
E. k(k+1)(k+2)
Math Expert V
Joined: 02 Aug 2009
Posts: 8190
Re: If k is an integer greater than 6, all of the following must be divisi  [#permalink]

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2
3
Vinayprajapati wrote:
IF K is an integer greater than 6, then all the following must be divisible by 3 EXCEPT
a) k(k+3)(k-1)
b)3k^3
c)(k+1)(k+5)(k+6)
d)(k+2)(k-2)(k+3)
e)k(k+1)(k+2)

Since we are working with VARIABLE, We can be sure if the product can be shown as 3 consecutive numbers, by adding /subtracting 3 from any of the terms..

lets see the choices

a) k(k+3)(k-1)
(k-1)*k*(k+1) are consecutives BUT instead of k+1, we have k+3 in k(k+3)(k-1) ..
and if k+1 is div by 3, k+3 will not and k and k-1 will also be not div by 3..
so this is NOT necessary to be div by 3

b)3k^3
3 is there in the term, so TRUE

c)(k+1)(k+5)(k+6)
if K+1 is div by 3, k+1+3=k+4 will also be div by 3
so we have consecutive terms by adding 3 to k+1
k+4, k+5 and k+6..
TRUE

d)(k+2)(k-2)(k+3)
add 3 to k-2. it becomes k-2+3=k+1..
again 3 consecutive terms k+1, k+2 and k+3
TRUE

e)k(k+1)(k+2)
TRUE
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Math Expert V
Joined: 02 Sep 2009
Posts: 59147
Re: If k is an integer greater than 6, all of the following must be divisi  [#permalink]

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Vinayprajapati wrote:
IF K is an integer greater than 6, then all the following must be divisible by 3 EXCEPT
a) k(k+3)(k-1)
b)3k^3
c)(k+1)(k+5)(k+6)
d)(k+2)(k-2)(k+3)
e)k(k+1)(k+2)

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Re: If k is an integer greater than 6, all of the following must be divisi  [#permalink]

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I looked at this question and thought why would somebody make this question and post it here. then I saw that it is from GMATPREP. So now i assume this is one of those simple questions that make you think about your performance while doing the CAT. Algorithm's tricks.
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Joined: 30 May 2015
Posts: 34
Re: If k is an integer greater than 6, all of the following must be divisi  [#permalink]

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I figured it out by taking K=7 and k=8
and option A is not divisible by 3 in case of k=8

Thanks !
Intern  B
Joined: 08 Feb 2017
Posts: 7
Location: United States
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Re: If k is an integer greater than 6, all of the following must be divisi  [#permalink]

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I still don't understand this one why it would be choice A.
Math Expert V
Joined: 02 Sep 2009
Posts: 59147
Re: If k is an integer greater than 6, all of the following must be divisi  [#permalink]

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2
kimbercs wrote:
I still don't understand this one why it would be choice A.

The question asks: If k is an integer greater than 6, then all the following must be divisible by 3 EXCEPT:

k(k+3)(k-1) (option A) is not necessarily divisible by 6. For example, if k = 8, then k(k+3)(k-1)=8*11*7, which is not divisible by 6. So, the answer is A.
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Re: If k is an integer greater than 6, all of the following must be divisi  [#permalink]

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Got it now. Thank you!
Director  G
Joined: 02 Sep 2016
Posts: 642
Re: If k is an integer greater than 6, all of the following must be divisi  [#permalink]

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chetan2u wrote:
Vinayprajapati wrote:
IF K is an integer greater than 6, then all the following must be divisible by 3 EXCEPT
a) k(k+3)(k-1)
b)3k^3
c)(k+1)(k+5)(k+6)
d)(k+2)(k-2)(k+3)
e)k(k+1)(k+2)

Since we are working with VARIABLE, We can be sure if the product can be shown as 3 consecutive numbers, by adding /subtracting 3 from any of the terms..

lets see the choices

a) k(k+3)(k-1)
(k-1)*k*(k+1) are consecutives BUT instead of k+1, we have k+3 in k(k+3)(k-1) ..
and if k+1 is div by 3, k+3 will not and k and k-1 will also be not div by 3..
so this is NOT necessary to be div by 3

b)3k^3
3 is there in the term, so TRUE

c)(k+1)(k+5)(k+6)
if K+1 is div by 3, k+1+3=k+4 will also be div by 3
so we have consecutive terms by adding 3 to k+1
k+4, k+5 and k+6..
TRUE

d)(k+2)(k-2)(k+3)
add 3 to k-2. it becomes k-2+3=k+1..
again 3 consecutive terms k+1, k+2 and k+3
TRUE

e)k(k+1)(k+2)
TRUE

When should one use plug in method to solve a question? Is this method of plugging in better?
VP  P
Joined: 07 Dec 2014
Posts: 1221
Re: If k is an integer greater than 6, all of the following must be divisi  [#permalink]

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Vinayprajapati wrote:
IF K is an integer greater than 6, then all the following must be divisible by 3 EXCEPT
a) k(k+3)(k-1)
b)3k^3
c)(k+1)(k+5)(k+6)
d)(k+2)(k-2)(k+3)
e)k(k+1)(k+2)

k(k+3)(k-1) will not be divisible by 3 when k=3n-1, where n is any positive integer
A
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WE: Management Consulting (Consulting)
Re: If k is an integer greater than 6, all of the following must be divisi  [#permalink]

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Just test k=11.

Each answer choice but A will lead to a set of numbers divisible by 3.
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+1 Kudos if I have helped you Re: If k is an integer greater than 6, all of the following must be divisi   [#permalink] 16 Oct 2019, 20:45
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